destiny vs bad luck

destiny and bad luck both are nouns.

Word	Noun	Adjective	Verb	Adverb
destiny	Yes	No	No	No
bad luck	Yes	No	No	No

As nouns, bad luck is a hyponym of destiny; that is, bad luck is a word with a more specific, narrower meaning than destiny:

destiny: your overall circumstances or condition in life (including everything that happens to you)
bad luck: an unfortunate state resulting from unfavorable outcomes

Other hyponyms of destiny include good fortune, good luck, luckiness, providence, ill luck, misfortune, tough luck, failure.

destiny (noun)	bad luck (noun)
an event (or a course of events) that will inevitably happen in the future	unnecessary and unforeseen trouble resulting from an unfortunate event
the ultimate agency regarded as predetermining the course of events	an unpredictable outcome that is unfortunate
your overall circumstances or condition in life (including everything that happens to you)	an unfortunate state resulting from unfavorable outcomes